Constructions of 2-Rotation Symmetric Semi-Bent Functions with Degree Bigger than 2

Qinglan ZHAO
Baodong QIN

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A    No.11    pp.1497-1503
Publication Date: 2019/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1497
Type of Manuscript: PAPER
Category: Cryptography and Information Security
Boolean functions,  2-rotation symmetric,  semi-bent functions,  algebraic degree,  

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Semi-bent functions have important applications in cryptography and coding theory. 2-rotation symmetric semi-bent functions are a class of semi-bent functions with the simplicity for efficient computation because of their invariance under 2-cyclic shift. However, no construction of 2-rotation symmetric semi-bent functions with algebraic degree bigger than 2 has been presented in the literature. In this paper, we introduce four classes of 2m-variable 2-rotation symmetric semi-bent functions including balanced ones. Two classes of 2-rotation symmetric semi-bent functions have algebraic degree from 3 to m for odd m≥3, and the other two classes have algebraic degree from 3 to m/2 for even m≥6 with m/2 being odd.